$95$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $55$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Solution: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 95}$ ${x = 2y-55}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-55}$ for $x$ in the first equation. ${(2y-55)}{+ y = 95}$ Simplify and solve for $y$ $ 2y-55 + y = 95 $ $ 3y-55 = 95 $ $ 3y = 150 $ $ y = \dfrac{150}{3} $ ${y = 50}$ Now that you know ${y = 50}$ , plug it back into ${x = 2y-55}$ to find $x$ ${x = 2}{(50)}{ - 55}$ $x = 100 - 55$ ${x = 45}$ You can also plug ${y = 50}$ into ${x+y = 95}$ and get the same answer for $x$ ${x + }{(50)}{= 95}$ ${x = 45}$ There were $45$ home team fans and $50$ away team fans.